Q: What are the factor combinations of the number 21,104,123?

 A:
Positive:   1 x 2110412317 x 124141953 x 39819159 x 357697397 x 53159901 x 234231003 x 210413127 x 6749
Negative: -1 x -21104123-17 x -1241419-53 x -398191-59 x -357697-397 x -53159-901 x -23423-1003 x -21041-3127 x -6749


How do I find the factor combinations of the number 21,104,123?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 21,104,123, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 21,104,123
-1 -21,104,123

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 21,104,123.

Example:
1 x 21,104,123 = 21,104,123
and
-1 x -21,104,123 = 21,104,123
Notice both answers equal 21,104,123

With that explanation out of the way, let's continue. Next, we take the number 21,104,123 and divide it by 2:

21,104,123 ÷ 2 = 10,552,061.5

If the quotient is a whole number, then 2 and 10,552,061.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 21,104,123
-1 -21,104,123

Now, we try dividing 21,104,123 by 3:

21,104,123 ÷ 3 = 7,034,707.6667

If the quotient is a whole number, then 3 and 7,034,707.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 21,104,123
-1 -21,104,123

Let's try dividing by 4:

21,104,123 ÷ 4 = 5,276,030.75

If the quotient is a whole number, then 4 and 5,276,030.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 21,104,123
-1 21,104,123
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

11753593979011,0033,1276,74921,04123,42353,159357,697398,1911,241,41921,104,123
-1-17-53-59-397-901-1,003-3,127-6,749-21,041-23,423-53,159-357,697-398,191-1,241,419-21,104,123

More Examples

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